Dice loss gives binary output whereas binary crossentropy produces probability output map
The probability map / output isn't produced by your loss function, but your output layer, which is activated either by softmax or sigmoid. 

In other words, your dice loss output is also a probability map. It's simply very confident in itself. If you forget about the problem with potential overfitting for a moment and train your binary crossentropy model longer, the probability values will eventually all converge to the 2 ends (0 and 1). 

In my experience, dice loss and IOU tend to converge much faster than binary crossentropy for semantic segmentation, so if you stop the training early on, dice loss will produce a probability map that resembles a binarized output more so than binary crossentropy.